CP Violation in the B Meson System: Recent Experimental Results 1

CP violation in the B meson system: recent experimental results

Gautier Hamel de Monchenault CEA/DSM/DAPNIA/SPP Saclay, F-91191 Gif-sur-Yvette Cedex, France

Published in Proceedings of the EPS International Conference on High Energy Physics, Budapest, 2001 (D. Horvath, P. Levai, A. Patkos, eds.), JHEP (http://jhep.sissa.it/) Proceedings Section, PrHEP-hep2001/293.

Abstract

Recent experimental results on CP violation in the study of B meson decays are reviewed. The emphasis is put on the recent measurements of the CP parameter sin2β by the BABAR and BELLE experiments at asymmetric B factories, which establish for the ﬁrst time CP violation in the B meson system.

1 Introduction

CP violation has been extensively studied in the K0 system since the discov- 0 ery of the phenomenon in KL decays thirty seven years ago [1], while the last ﬁfteen years have been rich in experimental and theoretical developments in Heavy Flavor physics [2]. The consistency of the experimental results with the general scheme of charged weak interactions and CP violation in the Standard Model of particle physics is highly non-trivial. Now is the time to challenge the model experimentally in its prediction of large CP violation eﬀects in the B meson system. This paper gives an overview of the present experimental knowledge on the subject. We start with a status report on the new generation of B factory experiments, followed by an introduction

1 to the B0B0 system and the CKM matrix, and an overview of present experimental constraints on the Unitarity Triangle from CP -violating K and CP -conserving B observations. We then review in turn searches for CP violation in the B system: direct CP violation, CP violation in B0B0 mixing and, ﬁnally, CP violation in the interference between mixing and decay, with an emphasis on the recent sin2β measurements by BABAR and BELLE. We conclude the review by an overview of experimental prospects in the domain.

2 Status of B factory experiments

+ The three e e− B factories in activity are CESR at Cornell, PEP-II at + SLAC and KEK-B at KEK at which B meson pairs are produced in e e− annihilations in the Υ (4S) resonance energy region at √s 10.58 GeV. The new-generation machines, PEP-II and KEK-B, are energy-asymmetric:≈ the electron and positron beams are stored at diﬀerent energies in two separate storage rings so that the proper time diﬀerence between the two B meson decays can be deduced from the measurable distance between the two decay vertices along the boost axis. Both machines have started operation in late Spring 1999 and have improved steadily their performances. At the time of the Conference in July 2001, the two machines had already demon- strated very high instantaneous luminosities with tolerable backgrounds for the detectors: 4.5 1033 cm 2s 1 for KEK-B (for a design luminosity of 1034) × − − and 3.5 1033 for PEP-II(already beyond the design luminosity of 3 1033). × × The data samples recorded by the BABAR and BELLE experiments were of 1 comparable size: about 30 fb− at the Υ (4S) resonance (corresponding to about 32 million BB pairs).

3TheB0B0 system

The light BL and heavy BH mass eigenstates of the neutral Bd meson system (made of b and d quarks) are given by 1:

B = p B0 + q B0 , B = p B0 q B0 . (1) | Li | i | i | H i | i− | i where B0 and B0 are the flavor eigenstates of the system, related through CP transformation according to: CP B0 = e2iξB B0 (the phase ξ is | i | i B arbitrary, due to b-flavor conservation by strong interactions). The complex coefficients p and q are normalized ( p 2 + q 2 = 1). The phase of q/p,which | | | | 1CP T invariance is assumed throughout this paper

2 also depends on phase conventions, is not an observable; only the modulus of this quantity, p/q , has a physical significance. | | The mass difference ∆mBd and width difference ∆ΓBd between the two mass eigenstates are defined as:

∆m m m , ∆Γ Γ Γ . (2) Bd ≡ BH − BL Bd ≡ BH − BL Based on model-independent considerations, the two mesons are expected to have a negligible diﬀerence in lifetime, ∆Γ /Γ 10 2[3]. In particular, Bd Bd ∼ − ∆Γ /Γ x where x ∆m /Γ =0.73 0.05. Neglecting ∆Γ Bd Bd d d ≡ Bd Bd ± Bd versus ∆mBd the time evolution of a state prepared initially (i.e. at time t = 0) in a pure B0 or B0 state, respectively, can be written as follows :

0 imt Γt/2 0 0 B (t) = e− e− cos ( ∆m t/2) B + i (q/p)sin(∆m t/2) B | phys i { Bd | i Bd | i} 0 imt Γt/2 0 0 B (t) = e− e− cos ( ∆m t/2) B + i (p/q)sin(∆m t/2) B (3) | phys i { Bd | i Bd | i} 1 1 where m = 2 (mBH + mBL )andΓ=2 (ΓBH +ΓBL ).

4 CP violation in the Standard Model

In the Standard Model of strong and electro-weak interactions, CP violation arises from the presence of a single irremovable phase in the unitary complex mixing matrix for the three quark generations [4][5]. This phase is called the Kobayashi-Maskawa phase, and the matrix, the Cabibbo-Kobayashi- Maskawa (CKM) mixing matrix. The unitarity of the CKM matrix can be expressed in geometric form as six triangles of equal areas in the complex plane. A non-zero area directly implies the existence of a CP -violating phase [6]. One of the six triangles, the Unitarity Triangle, represents the most experimentally accessible of the unitarity relations, which involves the two smallest elements of the CKM matrix, V and V . V is involved in b u transitions such as in B meson ub td ub → decays to charmless ﬁnal states, and Vtd appears in b d transitions that can proceed via diagrams involving virtual top quarks,→ examples of which are the box diagrams describing the B0B0 mixing. Because the lengths of the sides of the Unitarity Triangle are of the same order, the angles can be large, leading to potentially large CP -violating asymmetries from phases between CKM matrix elements. The CKM matrix can be described by four real parameters. Using the sine of the Cabibbo angle λ as an expansion parameter, the Wolfenstein

3 parameterization is given by [7]:

2 3 Vud Vus Vub 1 λ /2 λAλ(ρ iη) − 2 −2 4 VCKM = V Vcs V  =  λ 1 λ /2 Aλ  + (λ ) , cd cb − − O V V V Aλ3(1 ρ iη) Aλ2 1  td ts tb   − − −  (4) where A,¯ρ = ρ(1 λ2/2) andη ¯ = η(1 λ2/2) are the remaining three parameters. It should− be noted that, in− this parameterization, the usual (but arbitrary) phase convention under which all the CKM matrix elements are real except Vub and Vtd is implicitly made.

5 Experimental situation before the B factories

The sine of the Cabibbo angle λ is known at the percent level (λ 0.2230). ' The parameter A, determined mostly from measurements of semileptonic decays of strange and beauty particles, is known at the 5% level (A ' 0.830). The coordinates of the apex of the Unitarity Triangle,ρ ¯ andη ¯, are constrained by ε , V /V ,∆m measurements, and by the limit | K | | ub cb| Bd on ∆mBd /∆mBs . These constraints depend on additional measurements and theoretical inputs. Many critical studies of the CKM constraints are available in the recent literature (see for instance Ref. [8]-[13]); they diﬀer in the way theoretical uncertainties and experimental systematic errors are handled, and in the statistical treatment in the combination of the available information. The conclusions of the various analyses are quite consistent however [1]. Reference [8] for instance gives 95% conﬁdence intervalsρ ¯ ∈ [0.04, 0.38] andη ¯ [0.21, 0.49]. The allowed range forη ¯ is an experimental indication that the∈ CKM matrix indeed contains a non-zero phase.

The side of the Unitarity Triangle that is proportional to VtdVtb∗ forms an angle β with the side proportional to VcdVcb∗ andanangleα with the side proportional to VudVub∗ . Experimental sensitivity to the angles β and α can therefore arise from interferences between the B0B0 mixing amplitude (which involves Vtd) and decay amplitudes that involve Vcb and Vub respectively. The third angle, γ, is the argument of Vub∗ in the usual phase convention. The experimental programme for testing the CKM model with three generations of leptons, in particular its description of CP violation in the charged weak current sector, involves as many measurements of the sides, angles and other quantities constraining the position of the apex of the Unitarity Triangle, and checking that the results are indeed consistent. The CP -violating observable sin2β is already constrained by the allowed region

4 CLEO [14] BABAR [15] BELLE [16] World average 0 + +1.6 +2.3 +0.89 B π π− 4.3 1.4 0.5 4.1 1.0 0.7 5.6 2.0 0.4 4.44 0.86 0 → + −+2.5± ± ± −+3.4±+1.5 −+1.47 B K π− 17.2 1.4 1.2 16.7 1.6 1.3 19.3 3.2 0.6 17.37 1.30 0 → + − ± ± ± − − − B K K− < 1.9 < 2.5 < 2.7 + → + 0 +2.0 B π π < 12.7 5.7 1.8 0.8 < 13.4 + → + 0 +3.0 +1.4 −+2.1± +3.5 +1.6 +1.70 B K π 11.6 2.7 1.3 10.8 1.9 1.0 16.3 3.3 1.8 12.13 1.67 + → 0 + +4−.6 − −+3.3 ± −+5.7 −+1.9 −+2.60 B K π 18.2 4.0 1.6 18.2 3.0 2.0 13.7 4.8 1.8 17.41 2.51 0 → 0 0 −+5.9±+2.4 +3− .1 ± −+7.2 −+2.5 −+2.66 B K π 14.6 5.1 3.3 8.2 2.7 1.2 16.0 5.6 2.7 10.73 2.66 → − − − ± − − − Table 1: Recent measurements of branching ratios for B meson decays to 6 charmless two-body ﬁnal states containing pions or kaons, in units of 10− . In certain cases, 90% conﬁdence limits are given.

in (¯ρ, η¯)fromCP -conserving measurements: sin2β [0.47, 0.89] at the 95% conﬁdence level [8]. ∈

6 CP violation in the decay

CP violation in the decay (also referred to as direct CP violation) is due to interference among decay amplitudes which diﬀer in both weak and strong 0 phases. Direct CP violation is now ﬁrmly established in KL decays: the amount of direct CP violation recently reported by NA48 and KTeV is consistent with predictions based on the Standard Model within large theoretical uncertainties [1]. For B decays, one builds time-independent CP asymmetry observables:

2 Γ( B f ) Γ( B f ) 1 Af /Af CP → − → = −| | . (5) A ≡ Γ( B f )+Γ(B f ) 1+ A /A 2 → → | f f | Direct CP violation is the only type of CP violation for charged modes, while for neutral modes it competes with the other two types of CP violation.

Sizable direct CP violation effects ( Af /Af = 1) require the contribution to the decay of at least two amplitudes| of|6 comparable size with of course different weak phases, but also a non-zero relative strong phase (the latter is in general difficult to estimate theoretically). The rule of thumb is that larger CP violation effects are potentially expected for very rare processes for which the dominant amplitude (e.g. a tree amplitude) is suppressed at the level of higher-order amplitudes (e.g. penguin amplitudes).

5 CLEO [17] BABAR [15] [52] BELLE [18] +0.19 B K±π∓ 0.04 0.16 0.19 0.10 0.04 0.17 → 0 − ± − ± −+0.22 B± K±π 0.29 0.23 0.00 0.18 0.06 0.20 → 0 − ± ± − +0− .43 B± Ks π± 0.18 0.24 0.21 0.18 0.10 0.34 → ± − ± − Table 2: Recent measurements of charge CP asymmetries in self-tagged B Kπ decay modes. →

In charmless hadronic decays for instance, the tree b u amplitude is → highly suppressed and competes with b s or b d penguin amplitudes: → → asymmetries for these modes could be as large as 10%. The various B ππ → and B Kπ modes have all been recently observed by CLEO [14] and → confirmed by BABAR [15] and BELLE [16] (see Table 6), with branching ratios 6 5 in the 10− -10− region. CP asymmetries in the self-tagged modes have been measured [15][17][18] consistent with zero within errors (see Table 6). CP asymmetries have also been measured in a variety of other charmless B decays [19] and again no significant deviation from zero has been observed. For all these modes, the sensitivity on CP is at best at the 10%-15% level. Is is interesting to look for asymmetriesA where none is expected. Ex- amples are the loop-induced b sγ modes, for which CP is strongly suppressed within the Standard Model.→ Combining two statisticallyA independent measurements, one based on the pseudo-reconstruction of the Xs system, the other on tagging the flavor of the other B with leptons, CLEO measures [20]: (b sγ)= 0.079 0.108 0.022. CP asymmetries have also ACP → − ± ± been measured the exclusive B K γ mode by CLEO and BABAR [21]: ± → ∗± (B K γ)=+0.08 0.13 0.03 and 0.035 0.076 0.012, re- ACP ± → ∗± ± ± − ± ± spectively. In both inclusive and exclusive b sγ analyses, much higher → statistics are needed to challenge the SM on the prediction of very small CP asymmetries. Similarly, an order of magnitude more data would be needed to test the prediction of a strong suppression in pure penguin b sss ACP → decays, such as the recently observed B φK modes [22][23][24]. → The copious b ccs decays are in general dominated by the tree am- → plitude. In modes such as B± J/ψK ±, the tree amplitude is colored- suppressed but the dominant penguin→ contribution has nearly the same weak phase and direct CP violation further suppressed. This is experimentally confirmed at the 4% level by CLEO [25]: (B J/ψK )=(+1.8 ACP ± → ± ± 4.3 0.4)% and at the 3% level by BABAR [21]: (B J/ψK )= ± ACP ± → ± ( 0.9 2.7 0.5)%. − ± ±

6 7 CP violation in mixing

CP (or T ) violation in B0B0 mixing (also referred to as indirect CP violation) manifests itself as an asymmetry in the transitions B0 B0 and B0 → → B0, as a consequence of the mass eigenstates being diﬀerent from the CP eigenstates:

q/p =1 = Prob(B0 (t) B0) =Prob(B0 (t) B0) . | |6 ⇒ phys → 6 phys → This effect can be studied by investigating time-dependent differences in mixing rates in decays to flavor-specific final states such as semileptonic neutral B decays:

0 + 0 Γ( Bphys(t) ` νX ) Γ( Bphys(t) `−νX ) T (t)= | i→ − | i→ . (6) A Γ( B0 (t) `+νX )+Γ( B0 (t) ` νX ) | phys i→ | phys i→ − Starting from equations 3, one ﬁnds that the proper time dependence cancels out in the ratio 6 and the asymmetry is independent of t:

1 q/p 4 (t)=a with a −| | . (7) AT T T ≡ 1+ q/p 4 | | The CP asymmetry parameter aT can be extracted from both time-integrated and time-dependent measurements. At LEP and the Tevatron, time-dependent asymmetries are studied using either ﬂavor-tagged samples of semileptonic decays or fully inclusive samples of B0 decays. In the latter case, the time-integrated rate vanishes due to CP T symmetry but some sensitivity to aT exists in the time-dependence of the asymmetry, as shown in Ref. [26]. Averaging the results of their various analyses, CDF [27], OPAL [28] and ALEPH [29] obtain a =0.024 0.063 0.033, a =0.004 0.056 0.012 T ± ± T ± ± and aT = 0.013 0.026(stat + syst), respectively. At the Υ (4S), CLEO has recently measured− ± the integrated like-sign dilepton charge asymmetry [30]; the result is in agreement with its previous measurement of aT via partial hadronic reconstruction. The weighted average of the two CLEO measurements gives: aT =0.014 0.041 0.006. At this Conference, BABAR has presented a time-dependent± analysis± of its like-sign dilepton sample based 1 on 20.7 fb− of data [31], obtaining: a =0.0048 0.0116 0.0144. This T ± ± preliminary result demonstrates that asymmetric B factory experiments are already close to sensitivities needed to test theoretical predictions on 2 indirect CP violation (aT 10− ), and that systematic uncertainties can be controlled at the required≤ level.

7 To conclude, no signiﬁcant indirect CP violation eﬀect in the neutral B meson system has been seen to date. This experimental constraint allows us to express, to a very good approximation, the ratio q/p in term of a pure 2iφ 2iξ phase φM : q/p = e M e B (ξB is maintained to express the arbitrariness of the phase convention). The phase φM results from CKM factors involved in the box diagrams that describe the dispersive part of the B0 B0 amplitude. In the Standard Model, to a very good approximation: →

q VtdV ∗ = tb e2iξB (8) p Vtd∗ Vtb and therefore φ =arg(V V )=π β +arg(V V ), which, in the usual M td tb∗ − cd cb∗ phase convention, reduces to φM = β. New Physics can possibly manifest itself as a phase shift with respect− to the Standard Model expectation for φM .

8 CP violation in interference between decay with/without mixing

In order to calculate the time-dependent decay rates to a speciﬁc ﬁnal state f accessible to both B0 and B0 decays, one introduces the phase-independent complex parameter λf :

q Af λf , (9) ≡ p Af where A f H B0 and A f H B0 . Particularly interesting is the f ≡h | | i f ≡h | | i situation where A 2 A 2. This condition is fulﬁlled in the case that | f | ≈| f | we consider now, where the ﬁnal state f is a CP eigenstate, fCP .Using equations 3, one obtains

1 2 1 2 Γt ρ (t)= 1+ λf 1 λf cos (∆mB t) Im(λf )sin(∆mB t) e− , ± 2 | CP | ± 2 −| CP | d ∓ CP d (10)

0 2 2 0 2 2 with ρ+(t) fCP H Bphys(t) / AfCP and ρ (t) fCP H Bphys(t) / AfCP . ≡|h | | i| | | − ≡|h | | i| | | One ﬁnds that the conditions for no CP violation at any time t are λ =1 | fCP | and Im λfCP =0:

λ = 1= Prob(B0 (t) f ) =Prob(B0 (t) f ) . (11) fCP 6 ± ⇒ phys → CP 6 phys → CP

8 The time-dependent CP asymmetry:

0 0 Γ( Bphys(t) fCP ) Γ( Bphys(t) fCP ) f (t) | i→ − | i→ (12) A CP ≡ Γ( B0 (t) f )+Γ( B0 (t) f ) | phys i→ CP | phys i→ CP can be written as:

(t)=S sin (∆m t) C cos (∆m t) , (13) AfCP fCP · Bd − fCP · Bd where the coeﬃcients of the sine and cosine terms are: 2Imλ 1 λ 2 S = fCP and C = −| fCP | . (14) fCP 1+ λ 2 fCP 1+ λ 2 | fCP | | fCP | The cosine term vanishes in absence of both CP violation in mixing ( q/p = | | 1) and direct CP violation in the decay ( A /A = 1). Even in that | fCP fCP | case, CP violation can arise from the weak phase diﬀerence between q/p and

AfCP /AfCP , resulting in a non-vanishing sine term (Im λfCP = 0). In the language of ﬂavor eigenstates, this is interpreted as an interference6 between the decay of a B0 meson with and without mixing 2. In the case of a single CP -violating phase in the disintegration process, φD, one ﬁnds:

A fCP 2iφD 2iξB = ηfCP e e− , (15) AfCP where ηfCP is the CP parity of the fCP ﬁnal state, ηfCP = 1. It follows that: ±

2i(φD+φM ) λfCP = ηfCP e ,SfCP =ImλfCP = ηfCP sin 2(φD + φM ),CfCP =0, (16) and

(t)=η sin 2(φ + φ )sin(∆m t) . (17) AfCP fCP D M Bd 0 The ”gold-plated” J/ψK S,L modes provide a theoretically clean way of 4 extracting sin2β: the branching ratio are relatively high ( 10− )andthe experimental signatures are clear. The quark subprocess∼ at the tree level for the B0 J/ψ K0 is b ccs, which involves the V V product of CKM → → cs∗ cb 2note that, if the interpretation of this CP -violating eﬀect is somewhat convention- dependent, the phase of λfCP is not.

9 factors. The interference in B0(B0) J/ψK 0 is possible due to K0K0 → S,L mixing which introduces another CKM product, Vcd∗ Vcs. With negligible theoretical uncertainty, direct CP violation is ruled out in these modes (this is supported experimentally by the non-observation of direct CP violation in the SU(3)-related B J/ψK decay). In the usual phase convention, ± → ± the ratio of amplitudes is made real, φD = 0, and all the eﬀect comes from the phase φ = β in q/p, i.e. from the fact that the mass eigenstates are M − not CP -even and CP -odd. One ﬁnds:

0 0 J/ψK = ηJ/ψK sin 2β sin (∆mBd t) , (18) A S,L − S,L where η 0 and η 0 are equal to 1 and +1, respectively. At LEP, J/ψK S J/ψK L 0 0 − OPAL [32] with 24 B J/ψK S candidates (60% purity) selected out of 0 → +1.8 4.4 million hadronic Z decays measures: sin2β =3.2 2.0(stat) 0.5(syst). ALEPH [33] with 23 candidates (71% purity) selected− out of± 4 million 0 +0.82 hadronic Z decays measures: sin2β =0.84 1.04(stat) 0.16(syst). At the −0 ±0 Tevatron (FNAL), CDF [34] using 400 B J/ψK S events out of the 1 → entire Run I data sample (110 pb− at √s =1.8 TeV) measures: sin2β = +0.41 0.79 0.44(stat + syst). − 8.1 The concept of an asymmetric B factory + The cleanest source of B mesons is in e e− collisions at the energy of the Υ (4S) resonance (√s 10.58 GeV). The Υ (4S) resonance is the lightest Υ ≈ PC resonance (bb bound state with J =1−−)aboveB meson pair production + threshold. To present knowledge, the Υ (4S) decays exclusively into B B− 0 0 + or B B final states in equal amounts. The e e− Υ (4S) process, with a cross-section close to 1 nb, competes with the QED→ pair production of light + quarks e e− qq (where q =u, d, s or c). The background from QED continuum constitutes→ 75% of the hadronic cross-section, but can be reduced thanks to distinct topological characteristics. Furthermore, the QED continuum can be studied with data taken at energies under the BB threshold, typically 40 MeV below the Υ (4S) resonance (off-resonance data). Due to the intrinsic spin of the Υ (4S), BB states produced in the Υ (4S) BB reaction are in a coherent L = 1 state. In the case of the → Υ (4S) B0B0 reaction, each meson evolves according to the time evolu- → tion of single B meson equations 3. However, the two mesons evolve in phase, and the correlation between both sides of the B0B0 system holds at any time after production until one of the two mesons decays. If the first meson decays into a flavor specific decay mode, the other meson in the pair,

10 at that same instant, must have the opposite flavor. If the first meson decays into a CP eigenstate, the other meson in the pair, at that same instant, must have opposite CP . Let us consider the case where one of the two mesons (called Btag) decays into a flavor-specific final state at proper time ttag, while the other meson (called Brec, because it is usually fully-reconstructed) decays into the final state f at proper time trec. After integration on trec + ttag, the decay rate writes:

∆t /τB 2 2 ρ(∆t, εtag) e−| | d ( A + A ) ∝ ·{ | f | | f | q 2 2 + εtag [2Im( A∗ A )sin(∆m ∆t) ( A A )cos(∆m ∆t)] ,(19) p f f Bd − | f | −| f | Bd } where ∆t = trec ttag is the proper decay time difference and εtag equals 1 − 0 0 or 1 depending or whether the Btag is identified as a B or a B . − If the final state f is also a flavor-specific final state (Brec = Bflav), one obtains from the above equation the normalized B0B0 mixing time distribution:

1 ∆ t /τBd h(∆t, εtag εf )= e−| | 1 εtag εf cos (∆mBd ∆t) , (20) × 4τBd { − × · }

0 where εf =+1or 1 depending on whether f is a B decay final state 0 − ( A =0)oraB decay final state ( A = 0). The cases εtag ε =+1 | f | | f | × f and εtag εf = 1 define the mixed and the unmixed samples, respectively. (If one considers× − the mixed and unmixed samples together, one obtains a pure lifetime distribution.) Similarly, if the final state f is a CP eigenstate (Brec = BCP ), the normalized decay distributions writes:

1 ∆ t /τBd f(∆t, εtag)= e−| | 1+εtag (SfCP sin ∆mBd ∆t CfCP cos ∆mBd ∆t) . 4τBd { · − · } (21)

The time distributions at the Υ (4S) are therefore obtained by substituting the proper time difference ∆t to the B0 decay time t, with the difference that ∆t is an algebraic quantity which takes values from to + .When −∞ ∞ integrating over ∆t, one loses the information on the coefficient of the sine term. As a result of the coherent production of B0 mesons at the Υ (4S), a time-integrated CP asymmetry measurement is insensitive to Im(λfCP ); the study the CP asymmetry as a function of ∆t is required. Experimentally, the variable ∆t can be related to the distance between the locations of the two B meson decays. In practice, at an energy-symmetric machine like CESR,

11 the ﬂight distance of the B mesons ( 30 µm) is too small compared to the interaction region size, and such a time-dependent∼ study is impossible even with perfect vertex resolution.

0.9

0.8 BABAR

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 1000 2000 3000 ∆z (µm)

Figure 1: Time-dependent relative rate of unlike-sign dilepton events 1 (BABAR data, 20.7fb− ) and the overlaid binned maximum likelihood ﬁt 0 0 from which the B B oscillation frequency ∆md is measured [36]: ∆mBd = 0.499 0.010 0.012 ¯h ps 1. The full scale, expressed here in µm, covers ± ± − more than 15 lifetimes of the B0 meson (about 1.5 oscillation period).

In the late 1980s, to resolve this problem, the concept of a machine op- erating at the Υ (4S)inanasymmetricmode,i.e. with beams of unequal energies, was proposed [35]. PEP-II and KEK-B were built on this model. At asymmetric B factories, the Υ (4S) is produced in motion in the labo- ratory frame, and the two B mesons travel measurable distances along the

12 boost axis before they decay. The relation between the proper time diﬀer- ence ∆t and the distance between the two B decay vertices along the boost axis ∆z is (to a very good approximation) ∆z = βγc∆t. The center-of-mass frame boosts for PEP-II and KEK-B are similar: βγ =0.56 and βγ =0.45, respectively. One lifetime of the B0 meson corresponds to a distance of the order of 250 µm along the boost axis and a complete B0 B0 mixing period

2π/∆mBd to about 2 mm. (This is illustrated on Fig. 1, which shows the time-dependent `±`∓ relative rate for dilepton events in BABAR data as a function of ∆z.) Time-dependent CP asymmetries are expected to be max- imal when mixed and unmixed samples are of equal size, around a quarter period ( 500 µm). ∼ 8.2 Mis-tagging probability and time-resolution function

Flavor tagging of selected events requires the determination of εtag, the flavor 3 of the Btag . In practice, of course, flavor tagging is imperfect. Let w be the probability for a signal event to be incorrectly assigned a flavor tag εtag.The perfect time-dependent probability density for this event ρ(∆t, εtag)hasto be replaced by (1 w) ρ(∆t, εtag)+w ρ(∆t, εtag)=ρ(∆t, (1 2w) εtag), − × × − − × whereweusethefactthatρ is linear in εtag. The effect of the imperfect flavor tagging is therefore to replace εtag by εtag in front of oscillatory D× terms in Eq. 19- 21, where 1 2w is a dilution factor due to mis-tagging. Flavor tagging is principallyD≡ − based on charge correlations of daughter particles with the flavor of the decaying Btag. For example, the presence 0 of the following particles would identify a B decay: high-momentum `− leptons (e and µ )fromb c` ν semileptonic decays; intermediate- − − → − momentum `+ lepton from cascade decays; K+ from charm decays; high- momentum π from B0 D +π decays; soft π+ from D + D0π+ − → ∗ − ∗ → decays. BABAR and BELLE use different strategies to combine this information. BABAR defines four tagging categories based on the physical content of the event (such as the presence of a lepton or a kaon) while BELLE uses a multi-dimensional likelihood method and defines six tagging categories based on the value of a continuous flavor tagging dilution factor. The tagging performances of the two experiments are very similar, with an effective tagging efficiency Q 27% (this means that a sample of 100 signal events is statistically equivalent≈ to a sample of 27 perfectly tagged events). The vertex resolution in z for the fully-reconstructed Brec is of the order of 60 µm, depending on the mode. The position of the vertex of the Btag 3thanks to the coherent evolution of B0 mesons at the Υ (4S), tagging the flavor of the Btag when it decays is equivalent to tagging the flavor of the Brec at ∆t =0.

13 is determined using the charged tracks not belonging to the Brec,andby exploiting energy-momentum conservation and the knowledge of the beam spot position. A precision on ∆z of the order of 180 µm is obtained (this is to be compared to the average flight distance 250 µm). The ∆z determination algorithms have high efficiencies, typically∼ greater than 97%. The final probability density functions %(∆t) are obtained by convoluting the ideal time distributions ρ(∆t) with a time resolution function (δ∆ ): R t + ∞ %(∆t) (ρ )(∆t)= ρ(∆t) (δ∆t) dδ∆t , (22) ≡ ⊗R Z ×R · −∞ where δ∆ =∆t ∆ttrue. The time resolution functions are parameterized as t − a normalized sum of two (BELLE) or three (BABAR ) Gaussian distributions with different means and widths. (In BABAR , the third Gaussian has a fixed very large width and no offset, and accounts for fewer than 1% of events with badly reconstructed vertices.) In both analyses, the core and tail distributions are allowed to have non-zero means to account for the bias due to the flight of charm particles whose decay products are used to determine the position of the Btag decay vertex, and their widths are scaled by event-by-event errors derived from the vertex fits. In BABAR ,the parameters of the resolution function are evaluated independently for each tagging category.

8.3 Flavor and CP samples

The flavor Bflav sample (Fig. 2) is composed of events where the final state f is a flavor-specific hadronic state, such as B0 D( ) π+, D( ) ρ+, D( ) a+, → ∗ − ∗ − ∗ − 1 J/ψK 0( K+π ) and charge conjugates. (Similar decay modes are con- ∗ → − sidered for charged B mesons.) The selection rate for these Cabbibo-favored 1 modes is of the order of 300 events per fb− , with purities around 85%. The CP sample is divided into three categories: η = 1, η =+1 CP − CP and mixed-CP . BELLE uses all selected events for the CP sample while BABAR applies further cuts, rejecting 30% of events with poor or very poor flavor tagging information. The ηCP = 1 sample (Fig. 3) is composed 0 0 − 0 0 of events selected in the B J/ψK S , ψ(2S)KS and χc1KS modes. Are → + 0 + considered the decays: J/ψ ` `−; KS π π− (and in certain cases 0 0 + → + → π π ); ψ(2S) ` ` and J/ψπ π ; χ 1 J/ψγ . BELLE also considers → − − c → B0 η K0 decays, with η K0Kπ and K+K π0. BELLE selects 706 → c S c → S − events with 93% purity, while BABAR keeps 480 events with 96% purity after tagging cuts. The ηCP = +1 sample is composed of events selected in the B0 J/ψK 0 mode: 569 events with 60% purity for BELLE and → L 14 2

1400 BABAR

1200

1000Events / 1 MeV/c

800

600

400

200

0 5200 5210 5220 5230 5240 5250 5260 5270 5280 5290 5300 2 Beam-Energy Substituted Mass (MeV/c )

Figure 2: Mass distribution for BABAR ’s sample of flavor-specific fully- 0 reconstructed hadronic B decays, called the Bflav sample in the text. (The mass is computed with the beam energy substituted to the measured energy of the candidates.) This sample, composed of 9360 signal events selected 1 out of 29.1 fb− of data, is used for lifetime and mixing measurements (see text).

273 events for 51% purity after tagging cuts for BABAR . The mixed-CP sample is composed of events selected in the B0 J/ψK 0 mode with → ∗ K 0 K0π0: 41 events with 84% purity for BELLE and 50 events with 74% ∗ → S purity after tagging cuts for BABAR .ForthisVV mode, the CP content can be extracted from an analysis of angular distributions of the related non-CP J/ψK ∗ modes. BABAR [37] and BELLE [38] each use their own values of RT , the fraction of CP -odd in the decay. The results, R =0.16 0.03 0.03 T ± ± and RT =0.19 0.04 0.04, respectively, are consistent with less-precise previous measurements.± ±

The information on the interesting physical quantities (for instance τBd ,

∆mBd or sin2β) is extracted from un-binned maximum likelihood fits to the ∆t spectra of either flavor or CP samples (or a combination of the two samples) using the probability density functions defined above for the signal. The fits also include empirical descriptions of background ∆t distributions, the parameters of which are determined mostly from events in the sidebands of the signal region or from events selected in off-resonance data. τBd and

15 ) 2 c 200 Data BG

100

Events/(0.002 GeV/ 0 5.200 5.225 5.250 5.275 5.300 Beam Constrained Mass (GeV/c2)

Figure 3: Beam energy-constrained mass distribution for BELLE’s high- purity sample of ηCP = 1eventsforthesin2β ﬁt (706 events selected out 1 − of 30 fb− of data).

∆mBd are fixed to their PDG value [39] in the fits for sin2β.Themis- tagging probabilities and the parameters of the resolution function for the signal and the background are fit parameters. BABAR also fits for a possible 0 0 difference between B and B tags. For the fit to the J/ψK ∗ sample, BELLE includes the event-by-event information of the K∗ helicity angle in the CP fit. BABAR performs a global fit to the flavor and CP sample in order to get a correct estimate for the errors and their correlations: the largest correlation between sin2β and any combination of the other fitted parameters is found to be as small as 13%.

8.4 Observation of CP violationintheB meson system Lifetimes measurements with fully-reconstructed decays are performed using the first two building blocks of the sin2β analysis: the reconstruction of B mesons in flavor eigenstates, and the ∆z determination. Using its Bflav and charged B samples, BABAR has produced precision measurements of B0 and B lifetimes and their ratio at the 2% level [40]: τ 0 =1.546 0.032 ± B ± ± 0.022 ps, τ =1.673 0.032 0.023 ps and τ /τ 0 =1.082 0.026 B± ± ± B± B ± ± 0.012. BELLE has lifetime results using B D `ν semileptonic decays → ∗ with comparable precision [41]: τ 0 =1.55 0.02 ps, τ =1.64 0.03 ps. B B± Mixing measurements use in addition the third± building block which± is flavor tagging. Using its Bflav sample, BABAR [42] measures ∆m =0.519 Bd ± 0.020 0.016 ¯h ps 1 (see Fig. 6). ± −

16 The first results of BABAR and BELLE concerning B lifetimes and ∆mBd are not only consistent with world averages [39], but in many cases competitive in precision with the combination of all previous results. This constitutes an important demonstration of the feasibility of time-dependent studies at asymmetric B factories and validates the experimental technique for the sin2β measurement. Important byproducts of these measurements are the determination of the parameters of the time resolution function and of the mis-tagging probabilities. These quantities are evaluated from the data on the high-statistics flavor sample rather than determined from Monte-Carlo simulation. The results from BABAR [36][43] and BELLE [44] on sin2β are: sin2β =0.59 0.14 0.05 BABAR ± ± sin2β =0.99 0.14 0.06 BELLE ± ± These two results independently establish CP violation in the B meson system at more than 4 standard deviations. (There is an unpleasant 2σ discrep- ancy between the two results which will hopefully be resolved with increased statistics.) The CP violation effect is large, and can be seen from the raw time distributions (and the resulting time-dependent asymmetry) as a clear excess of εtag η = 1 tags (resp. εtag η = +1 tags) at positive (resp. × CP − × CP negative) ∆t values (see Fig. 4 and 5). Various cross-checks have been performed, including internal consistency of various sub-samples and tagging categories, null asymmetry with high statistics charged and Bflav samples, etc. Systematic uncertainties are small since the time resolution and the tagging performance are extracted from the data themselves. Main residual systematic uncertainties come from resolution models, vertex algorithms, detector misalignments and possible difference between the flavor and the CP samples. The contribution to the systematics from the fraction, shape and CP content of the background is 0 0 sizable for the J/ψK L and J/ψK ∗ modes, but is negligible overall. System- atics from the uncertainty on τBd and ∆mBd are negligible. Averaging these results with previous measurements from CDF, ALEPH and OPAL, one obtains sin2βWA =0.79 0.11(stat + syst). Figure 7 shows ± how the present knowledge of the sin2β parameter constrains the apex of the Unitarity Triangle in the (¯ρ, η¯) plane. The constraint from direct sin2β measurements is represented by four branches, due to the four-fold ambiguity in deriving a value of β from a measurement of sin2β; one of the four possible solutions, in the upper left quadrant, is obviously consistent with the allowed region determined from the interpretation of previous experimental results in the context of the Standard Model.

17 9 Prospects

At this point, the knowledge of sin2β is not accurate enough to reduce the allowed region in the (¯ρ, η¯) plane significantly. However, sin2β constitutes potentially one of the best constraints on the position of the apex of the Unitarity Triangle since, as opposed to other quantities, its measurement is not limited by theoretical uncertainties but by statistics. Future, highly precise, measurements of sin2β will allow a correspondingly precise test of the CKM model. The two teams at SLAC and KEK are presently accumulating data at a unprecedented high rate. PEP-II has recently (early October 2001) de- 1 livered a record 263 pb− of data in one day; KEK-B holds the record of + 33 1 1 instantaneous luminosity for an e e− collider, 4.9 10 cm− s− .Ifthe machines keep with their schedule, each experiment× should have registered 1 close to 100 fb− of data (with 10% to 15% off-resonance) by early summer 1 2002. The current results from BELLE and BABAR for roughly 30 fb− have stat a statistical uncertainty of σsin2β 0.14. Assuming no further improvements in reconstruction efficiency and data' analysis, we can infer statistical uncer- stat 1 tainties of σsin2β 0.08 for 100 fb− . Most of the systematic uncertainties will be reduced with' larger statistics, and other systematics dominated by detector effects are likely to improve as well. It is believed that the total syst systematic uncertainties can be controlled at the level of σsin2β 0.03 for 1 ' 100 fb− . The next round of sin2β measurements at B factories will still be statistics dominated.

9.1 Comparison of sin2β in other decay modes A comparison of the asymmetry in the pure penguin b sss decay B 0 → → φKS with that in b ccs decays is sensitive to new particles with complex → 0 1 couplings. Typically, the experiments can detect one φKS event for 2 fb− of data at the Υ (4S) [22][23][24]. Using the results from the sin2β measurement, and scaling from the observed yields in that mode, the estimated 0 stat 1 uncertainty using the φKS mode is σsin2β 0.56 for 100 fb− . Clearly, much larger statistics is needed to probe new physics' appearing in loop diagrams by the measurement of sin2β with that mode. Asymmetries in other modes such as B0 J/ψπ 0 can also potentially measure sin2β, but even larger → statistics are needed. The b ccd modes B0 D( )+D( ) can also (to → → ∗ ∗ − leading terms) measure sin2β: most of these modes have been observed by CLEO [45] and recently a ﬁrst measurement of the polarization in the VV mode B0 D +D has been presented [46]. → ∗ ∗−

18 9.2 Measurements of sin 2α 0 + The CP decay mode B π π− receives competing contributions from tree and penguin diagrams.→ If the decay were dominated by the tree amplitude, the asymmetry would be proportional to sin 2α. However, the competing penguin amplitudes have different weak phases and as a result, the CP asymmetry in this mode measures sin 2αeff =sin2(α + δpeng), where δpeng accounts for the penguin contribution. This contribution can in prin- ciple be estimated using isospin relations among B ππ amplitudes [47]. However, the so-called isospin analysis is in practice→ jeopardized by the requirement of measuring flavor-tagged branching ratios B0 π0π0 and 0 0 0 6 → B π π (which could be as small as 10− ), and by the possible contribution→ of electroweak penguin amplitudes. Methods have been developed to bound experimentally the penguin contribution from a limit on non-tagged 0 0 0 B π π [48]-[50]. Methods allowing the determination of δpeng theoretically,→ such as the QCD factorization [51], are promising but need to be confronted to experiment [1][2]. Experimentally, the measurement is significantly more challenging than that of sin2β: branching fraction of order 5 10 6, large background from continuum, competition with the 4-times × − more copious mode B0 K+π . BABAR has however performed the first → − measurement of the time-dependent CP asymmetry in this mode [52] based +12 + 1 on 65 11 signal π π− events selected out of 31 fb− of on-peak data: − +0.53 +0.45 Sππ =0.03 0.56 0.11,Cππ = 0.25 0.47 0.14 , (23) − ± − − ± where Sππ, the coefficient of the sine term (see Eq. 13), is equal to sin 2αeff . 1 From this result, one can anticipate with 100 fb− an error of the order of 0 0 0 0.30 on sin 2αeff (moreover, it is conceivable that the B π π mode will → be observed, and the B+ π+π0 confirmed). → 9.3 Measurements of γ The study of charmless two-body B decays into pions and kaons (such as B Kπ) offers methods for the determination of the CP angle γ.Non- → trivial constraints (bounds) on γ (which is the relative weak phase between tree and penguin amplitudes for these decays) can be extracted from CP - averaged ratios of branching fractions using only isospin considerations. The general analysis is however complicated by possible contribution of electroweak penguin amplitudes, SU(3) breaking effects and final state interactions, so that predictions suffer from some amount of model dependence (see for instance Ref. [51] and [53]). Different models make predictions on direct CP asymmetries in the B Kπ modes that can be tested experimentally. → 19 The combination of CKM angles 2β + γ can be measured in decays of the type B D π. Here, the basic idea is to exploit the interference be- → ∗ tween the direct decay, B0 D +π , and the decay after B0B0 mixing, → ∗ − B0 B0 D +π [54]. The difficulty with this approach is the necessity → → ∗ − of measuring the ratio r of the doubly-Cabibbo-suppressed to the dominant decay amplitudes, in order to interpret the small expected amplitude of the time-dependent asymmetry. To overcome the problems specific to this decay mode, several other strategies based on the mixing-induced interference between the dominant b cud and the suppressed b ucd process (the → → relative weak phase of which is γ), have been proposed [55][56]. Experimen- tally, analyses are based on both full and partial reconstruction techniques, where the ratio r is determined from measurements in related less-suppressed modes. Preliminary studies are encouraging: one can anticipate accuracies 1 σsin (2β+γ) of the order of 0.4 with 100 fb− . At longer term, the B DK modes can be exploited to extract the ± → ± CP angle γ (the relative weak phase between the b cus and b ucs quark level amplitudes contributing to these decays). The→ original→ construction suggested in [57] is using exact isospin relations which link the modes B 0 0 0 0 → DCP K, B D K and B D K (DCP represents a CP eigenstate), but suffers from→ intrinsic difficulties→ [58]; several variants of the original method have been proposed [59][60], but all require the measurement of very rare 7 processes, at the 10− level. In addition, this type of construction suffers from an eight-fold ambiguity in the value of γ, so even higher precision is necessary to separate the multiple solutions for γ. Experimentally, evidence for B D K decays has been reported [61]. → CP 10 Conclusions

The last two years have been rich in important experimental results on CP violation. The asymmetric B factories have come online with out- standing beginnings: the BABAR and BELLE collaborations have already published world class results in the domain of B physics, and have established independently CP violation in the B system. Their measurements 1 of sin2β, obtained with 30 fb− each, dominate the present world average, sin2βWA =0.79 0.11(stat + syst). The encouraging BABAR result on ± sin 2αeﬀ demonstrates the feasibility of time-dependent CP analyses with small signals and large backgrounds at B factories. The data samples are expected to be multiplied by three before next summer, and by ten in the next three years, bringing sensitivities to direct and indirect CP violation

20 effects to the level of theoretical expectations. Experiments at hadron collid- ers benefit from much higher statistics in B mesons (but with different levels of backgrounds and different systematics), and the possibility of studying the Bs system. The upgraded CDF and D0 experiments at the Tevatron are starting up again and will produce competitive measurements of sin2β and probably the measurement of xs, as soon as in 2002. The collider experiments of the next generation, BTeV at the Tevatron and LHCB at the LHC, are planned to come online around year 2006 . Complementary approaches of B factories and collider experiments will be needed to perform the rich programme of redundant precision measurements in the domain of charged weak interactions for testing the CKM sector of the Standard Model, and probing the origin of the CP violation phenomenon.

11 Acknowledgements

It is my pleasure to thank Masa Yamauchi, Karl Ecklund, Zoltan Ligeti, Martin Beneke for their help, as well as my BABAR colleagues for their support, in particular Georges London and Andreas H¨ocker.

References

[1] M. Beneke, CP violation (theory), in Proceedings of the EPS Interna- tional Conference on High Energy Physics, Budapest, 2001 (D. Horvath, P. Levai, A. Patkos, eds.), JHEP (http://jhep.sissa.it/) Proceed- ings Section, PrHEP-hep2001/294.

[2] Z. Ligeti, Status of Heavy Flavor physics, in Proceedings of the EPS International Conference on High Energy Physics, Budapest, 2001 (D. Horvath, P. Levai, A. Patkos, eds.), JHEP (http://jhep.sissa.it/) Proceedings Section, PrHEP-hep2001/290.

[3] I. Bigi et al., in CP Violation, C. Jarlskog ed., World Scientiﬁc, Singa- pore (1988).

[4] N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531; M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49 (1973) 652.

[5] The BABAR Physics Book, P.F. Harrison and H.R. Quinn editors, SLAC-R-504 (1998).

21 [6] C. Jarlskog, in CP Violation, C. Jarlskog ed., World Scientiﬁc, Singa- pore (1988).

[7] L. Wolfenstein, Phys. Rev. Lett. 51(1983)1945.

[8] A. H¨ocker et al., Eur. Phys. J. C21(2001) 225-259; hep-ph/0104062.

[9]D.AtwoodandA.Soni; hep-ph/0103197.

[10] S. Mele; hep-ph/0103040.

[11] M. Ciuchini et al.; hep-ex/0012308

[12] A.J. Buras et al., Phys. Lett. B 500 (2001) 161-167; hep-ph/0007085.

[13] M. Bargiotti et al., Nuovo Cim. 23 (2000) 1; hep-ph/0001293.

[14] D. Cronin-Hennessy et al., CLEO Collaboration, Phys. Rev. Lett. 85 (2000) 515; hep-ex/0001010 .

[15] B. Aubert et al., BABAR Collaboration, Phys. Rev. Lett. 87 (2001) 151802; hep-ex/0105001 .

[16] K. Abe et al., BELLE Collaboration, Phys. Rev. Lett. 87 (2001) 101801; hep-ex/0104030 .

[17] S. Chen et al., CLEO Collaboration, Phys. Rev. Lett. 85 (2000) 525; hep-ex/0001009 .

[18] K. Abe et al., BELLE Collaboration, to be published in Phys. Rev. D; hep-ex/0106095 .

[19] B. Aubert et al., BABAR Collaboration; hep-ex/0109006 .

[20] T.E. Coan et al., CLEO Collaboration, Phys. Rev. Lett. 86 (2001) 5661- 5665, hep-ex/0010075 .

[21] S. Menke, for the BABAR Collaboration, in Proceedings of the EPS International Conference on High Energy Physics, Budapest, 2001 (D. Horvath, P. Levai, A. Patkos, eds.), JHEP (http://jhep.sissa.it/) Proceedings Section, PrHEP-hep2001/071.

[22] R.A. Briere et al., CLEO Collaboration, Phys. Rev. Lett. 86 (2001) 3718-3721; hep-ex/0101032 .

22 [23] B. Aubert et al., BABAR Collaboration, Phys. Rev. Lett. 87 (2001) 151801; hep-ex/0105001 .

[24] K. Abe et al., BELLE Collaboration, BELLE-CONF-0113.

[25] G. Bonvicini et al., CLEO Collaboration, Phys. Rev. Lett. 84 (2000) 5940; hep-ex/0003004 .

[26] M. Beneke, G. Buchalla and I. Dunietz, Phys. Lett. B 393 (1997) 132.

[27] F. Abe et al., CDF Collaboration, Phys. Rev. D55(1997) 2546-2558;

[28] G. Abbiendi et al., OPAL Collaboration, Eur. Phys. J. C12(2000) 609-626; hep-ex/9901017 .

[29] R. Barate et al., ALEPH Collaboration, Eur. Phys. J. C20(2001) 431-443.

[30] D.E. Jaﬀe et al., CLEO Collaboration, Phys. Rev. Lett. 86 (2001) 5000- 5003; hep-ex/0101006 . J. Bartelt et al., CLEO Collaboration, Phys. Rev. Lett. 71 (1993) 1680.

[31] B. Aubert et al., BABAR Collaboration, contributed paper to the Inter- national Europhysics Conference on High Energy Physics, Budapest, July 12-18, 2001; hep-ex/0107059 .

[32] K. Ackerstaﬀ et al., OPAL Collaboration, Eur. Phys. J. C5(1998) 379-388.

[33] R. Barate et al., ALEPH Collaboration, Phys. Lett. B 492 (2000) 259- 274.

[34] T. Aﬀolder et al., CDF Collaboration, Phys. Rev. D61(2000) 072005; hep-ex/9909003 ;

[35] P. Oddone, in Proceedings of the UCLA Workshop: linear collider B0 B0 factory conceptual design, edited by D. Stork, World Scientiﬁc (1987) 243.

[36] C. Touramanis, for the BABAR Collaboration, in Proceedings of the EPS International Conference on High Energy Physics, Budapest, 2001 (D. Horvath, P. Levai, A. Patkos, eds.), JHEP (http://jhep.sissa.it/) Proceedings Section, PrHEP-hep2001/067.

23 [37] B. Aubert et al., BABAR Collaboration, submitted to Phys. Rev. Lett.; hep-ex/0107049 .

[38] K. Abe et al., BELLE Collaboration, BELLE-CONF-0105.

[39] D.E. Groom et al., Eur. Phys. J. C 151 (2000) 1-878.

[40] B. Aubert et al., BABAR Collaboration, to appear in Phys. Rev. Lett.; hep-ex/0107019 .

[41] S. Schrenk, for the BELLE Collaboration, in Proceedings of the EPS International Conference on High Energy Physics, Budapest, 2001 (D. Horvath, P. Levai, A. Patkos, eds.), JHEP (http://jhep.sissa.it/) Proceedings Section, PrHEP-hep2001/068.

[42] B. Aubert et al., BABAR Collaboration, contributed paper to the Inter- national Europhysics Conference on High Energy Physics, Budapest, July 12-18, 2001; hep-ex/0107036 .

[43] B. Aubert et al., BABAR Collaboration, Phys. Rev. Lett. 87 (2001) 091801; hep-ex/0107013 . See also: B. Aubert et al., BABAR Collab- oration, Phys. Rev. Lett. 86 (2001) 2515-2522; hep-ex/0102030 .

[44] K. Abe et al., BELLE Collaboration, Phys. Rev. Lett. 87 (2001) 091802; hep-ex/0107061 . See also: A. Abashian et al., BELLE Collaboration, Phys. Rev. Lett. 86 (2001) 2509-2514; hep-ex/0102018.v2 .

[45] E. Lipeles et al., CLEO Collaboration, Phys. Rev. D62(2000) 032005; hep-ex/0002065 .

[46] B. Aubert et al., BABAR Collaboration, submitted to the 9th Inter- national Symposium on Heavy Flavor, Caltech, Sept. 10-13, 2001; hep-ex/0109069 . See also: B. Aubert et al., BABAR Collaboration, contributed paper to the International Europhysics Conference on High Energy Physics, Budapest, July 12-18, 2001; hep-ex/0107057 .

[47] M. Gronau and D. London, Phys. Rev. Lett. 65 (1990) 3381-3384.

[48] Y. Grossman and H.R. Quinn, Phys. Rev. D58(1998) 017504.

[49] J. Charles, Phys. Rev. D59(1999) 051007; hep-ph/9806468.

[50] M. Gronau, D. London, N. Sinha and R. Sinha, Phys. Lett. B 514 (2001) 315-320; hep-ph/0105308.

24 [51] M. Beneke et al., Nucl. Phys. B 606 (2001) 245-321; hep-ph/0104110.

[52] B. Aubert et al., BABAR Collaboration, submitted to the 20th Interna- tional Symposium on Lepton and Photon Interactions at High Energies, Rome, July 23-28, 2001; hep-ex/0107074 .

[53] A.J. Buras and R. Fleischer, Eur. Phys. J. C11(1999) 93; hep-ph/9810260.

[54] R. Aleksan, I. Dunietz and B. Kayser, Z. Physik C54(1992) 653-660.

[55] D. London, N. Sinha and R. Sinha; hep-ph/0104157.

[56] M. Diehl and G. Hiller, Phys. Lett. B 517 (2001) 125-128; hep-ph/0105213.

[57] M. Gronau and D. Wyler, Phys. Lett. B 265 (1991) 172-176.

[58] D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78 (1997) 3257- 3260; hep-ph/9612433.

[59] D. Atwood, I. Dunietz and A. Soni, Phys. Rev. D63(2001) 036005; hep-ph/0008090.

[60] M. Gronau and J.L. Rosner, Phys. Lett. B 439 (1998) 171-175.

[61] K. Abe et al., BELLE Collaboration, BELLE-CONF-0108.

25 0 → ψ 0 B J/ KS 60 0 → ψ 0 B (2S)KS BABAR 0 → χ 0 B c1KS 234 B0 tags 40 − 246 B0 tags

0 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -5 0 5 ∆t (ps)

Figure 4: Time distributions and raw asymmetry for BABAR ’s ηCP = 1 sample with, superimposed, the projection of the un-binned maximum like-− lihood fits. The top plot shows the time distributions for the B0-tagged (triangles) and B0-tagged CP samples (squares). The bottom plot shows the resulting raw asymmetry, which is diluted with respect to Eq. 18 due to unperfect flavor tagging and finite time resolution.

26 . q ξf = +1

. 0.20 q ξf = −1 t) ∆ dN/d( . 0.10 /N 1

0.00 -8 -4 0 4 8 ∆t (ps)

Figure 5: Time distributions for BELLE’s full CP sample after background substraction, with, superimposed, the projection of the un-binned maximum likelihood ﬁt to each distribution (open circles: εtag η = 1 tags; full × CP − circles: εtag η = +1 tags). × CP

27 1 0.8 BABAR 0.6 0.4 Asymmetry 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 024681012 |∆t| (ps)

Figure 6: Time-dependent asymmetry for the flavor sample (BABAR , 1 20.7fb− ), with, superimposed, the projection of the un-binned maximum likelihood fit, from which a competitive measurement of the B0B0 mixing frequency is extracted (see text). This sample is included in the global fit for sin2β and dominates the determination of the mis-tagging probabilities and parameters of the time resolution function.

28 1 ∆ ∆ ∆ md ms/ md

∆m |ε | d K

β sin 2 WA

η 0

| | Vub/Vcb

|ε | K

-1

CKM f i t t e r

-1 0 1 2 ρ

Figure 7: Present constraints on the position of the apex of the Unitarity Triangle in the (¯ρ, η¯) plane [8]. The world average of direct measurements of sin2β, represented by green and yellow hatched regions corresponding to one and two statistical standard deviations, is not included in the determination of the allowed region for the apex of the Unitarity Triangle.